Date: Feb 15, 2005 4:48 PM
Author: Guess who
Subject: Re: Max. Income, Quadratic Equation

On Tue, 15 Feb 2005 04:49:05 GMT, "Darrell" <>

>>> A plane with 100 seats may be chartered for $200 per person plus a fee
>>> of $5 per person for each empty seat. What number of passengers will
>>> provide the maximum income?

>> Let p be the number of passengers and i the income then
>> i = p*200 + p*(100 - p)*5
>> = 700*p - 5p^2
>> and you need to maximize i. Note that it makes no sense to
>> differentiate i wrt p because neither is a continuous variable.

>That doesn't matter; for all intents and purposes the problem can be
>modelled by this (continuous) function.

Agreed. Any problem in misunderstanding can be avoided if algebra
[completing the square] is used instead in this instance.

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